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arXiv · 0811.0907

Detecting non-sinusoidal periodicities in observational data using multi-harmonic periodograms

Roman V. Baluev
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Abstract

We address the problem of assessing the statistical significance of candidate periodicities found using the so-called `multi-harmonic' periodogram, which is being used for detection of non-sinusoidal signals, and is based on the least-squares fitting of truncated Fourier series. The recent investigation (Baluev 2008) made for the Lomb-Scargle periodogram is extended to the more general multi-harmonic periodogram. As a result, closed and efficient analytic approximations to the false alarm probability, associated with multi-harmonic periodogram peaks, are obtained. The resulting analytic approximations are tested under various conditions using Monte Carlo simulations. The simulations showed a suitable precision and robustness of these approximations.

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Roman V. Baluev. 2009-02-13. Detecting non-sinusoidal periodicities in observational data using multi-harmonic periodograms. https://doi.org/10.1111/j.1365-2966.2009.14634.x

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